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Simplifying 4u2 + 16u = 37 Reorder the terms: 16u + 4u2 = 37 Solving 16u + 4u2 = 37 Solving for variable 'u'. Reorder the terms: -37 + 16u + 4u2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 16u + 4u2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + 4u + u2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 4u + 9.25 + u2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 4u + u2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 4u + u2 = 0 + 9.25 4u + u2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 4u + u2 = 9.25 The u term is 4u. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4u + 4 + u2 = 9.25 + 4 Reorder the terms: 4 + 4u + u2 = 9.25 + 4 Combine like terms: 9.25 + 4 = 13.25 4 + 4u + u2 = 13.25 Factor a perfect square on the left side: (u + 2)(u + 2) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (u + 2) equal to 3.640054945 and -3.640054945.Subproblem 1
u + 2 = 3.640054945 Simplifying u + 2 = 3.640054945 Reorder the terms: 2 + u = 3.640054945 Solving 2 + u = 3.640054945 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = 3.640054945 + -2 Combine like terms: 2 + -2 = 0 0 + u = 3.640054945 + -2 u = 3.640054945 + -2 Combine like terms: 3.640054945 + -2 = 1.640054945 u = 1.640054945 Simplifying u = 1.640054945Subproblem 2
u + 2 = -3.640054945 Simplifying u + 2 = -3.640054945 Reorder the terms: 2 + u = -3.640054945 Solving 2 + u = -3.640054945 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + u = -3.640054945 + -2 Combine like terms: 2 + -2 = 0 0 + u = -3.640054945 + -2 u = -3.640054945 + -2 Combine like terms: -3.640054945 + -2 = -5.640054945 u = -5.640054945 Simplifying u = -5.640054945Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.640054945, -5.640054945}
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